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  1. Program New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems

    Organizers: Kay Kirkpatrick (University of Illinois at Urbana-Champaign), Yvan Martel (École Polytechnique), Jonathan Mattingly (Duke University), Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice Sophia-Antipolis), Luc Rey-Bellet (University of Massachusetts, Amherst), LEAD Gigliola Staffilani (Massachusetts Institute of Technology), Daniel Tataru (University of California, Berkeley)

    The fundamental aim of this program is to bring together a core group of mathematicians from the general communities of nonlinear dispersive and stochastic partial differential equations whose research contains an underlying and unifying problem: quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems, and in various regimes. 

    In recent years there has been spectacular progress within both communities in the understanding of this common problem. The main efforts exercised, so far mostly in parallel, have generated an incredible number of deep results, that are not just beautiful mathematically, but are  also important to understand the complex natural phenomena around us.  Yet, many open questions and challenges remain ahead of us. Hosting the proposed program at MSRI would be the most effective venue to explore the specific questions at the core of the unifying theme and to have a focused and open exchange of ideas, connections and mathematical tools leading to potential new paradigms.  This special program will undoubtedly produce new and fundamental results in both areas, and possibly be the start of a new generation of researchers comfortable on both languages.

    Updated on Sep 15, 2015 05:25 PM PDT
  1. Workshop Theory of Neural Computation

    Organizers: Dmitri Chklovskii (Simons Foundation), David Eisenbud (MSRI - Mathematical Sciences Research Institute), Gary Marcus (New York University), LEAD Bruno Olshausen (University of California, Berkeley), Christos Papadimitriou (University of California, Berkeley), Terrence Sejnowski (Salk Institute for Biological Studies), Fritz Sommer (University of California, Berkeley)

    The theme of this workshop is on bringing theory into the study of neural networks---those in brains and those in machines.  We will soon have the capability to monitor activity and structure in the brain at unprecedented scales, but what will these data tell us?  It is unlikely that we will gain insight without some theoretical framework to guide our thinking of what to look for, and why.  Similarly, neural network models can now perform feats of language translation and pattern recognition far beyond what was possible a few years ago; but they have yet to shed new light on neurobiological mechanisms in part because there is only a limited theory of such computations.

    What are likely candidates for such theories? Do they already exist? And what is needed to more tightly integrate theoretical frameworks with empirical approaches?

    Updated on Oct 01, 2015 09:46 AM PDT
  2. Seminar Research Mini-course

    Updated on Sep 25, 2015 11:07 AM PDT
  3. Seminar Research Mini-course

    Created on Sep 03, 2015 03:35 PM PDT
  4. Seminar Research Seminar

    Created on Sep 03, 2015 03:50 PM PDT
  5. Workshop New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems

    Organizers: Jonathan Mattingly (Duke University), LEAD Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice Sophia-Antipolis), Luc Rey-Bellet (University of Massachusetts, Amherst), Daniel Tataru (University of California, Berkeley)

    This workshop serves to bring into focus the fundamental aim of the jumbo program by both a)  showcasing the spectacular progress in recent years in the study of both nonlinear dispersive as well as stochastic partial differential equations and b) bringing to the fore the key challenges for the future in quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems.  

    During the two weeks long workshop, we intertwine talks on a wide array of topics by some of the key researchers in both communities and aim at highlighting the most salient ideas, proofs and questions which are important and fertile for `cross-pollination’ between PDE and SPDE. Topics include:  Global dynamics and singularity formation for geometric and physical nonlinear wave and dispersive models (critical and supercritical regimes); dynamics of infinite dimensional systems (critical phenomena, multi scale dynamics and metastability); symplectic structures of infinite dimensional dynamical systems; randomization and long time dynamics, invariant Gibbs and weighted Wiener measures; derivation of effective dynamics in quantum systems; weak turbulence phenomena; optimization and learning algorithms: distributed, stochastic and parallel.

    Updated on Sep 28, 2015 11:14 AM PDT
  6. Workshop Modern Math Workshop 2015

    Organizers: LEAD Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Helen Chamberlin (Ohio State University), Ricardo Cortez (Tulane University), Sujit Ghosh (NC State University), Dagan Karp (Harvey Mudd College), Anne Pfister (MSRI - Mathematical Sciences Research Institute), Christian Ratsch (University of California), Ivelisse M. Rubio (University of Puerto Rico), Mariel Vazquez (University of California, Davis), Talithia Williams (Harvey Mudd College)

    As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to host their annual SACNAS pre-conference event, the 2015 Modern Math Workshop (MMW). The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhD’s in building their research networks.

    Updated on Sep 29, 2015 05:40 PM PDT
  7. Workshop Workshop on Combinatorial Games, in honor of Elwyn Berlekamp's 75th Birthday

    Organizers: David Eisenbud (MSRI - Mathematical Sciences Research Institute), LEAD Richard Guy (University of Calgary), Thane Plambeck (Counterwave, Inc.), Aaron Siegel (Twitter, Inc.)

    A two-day workshop with research-level talks on combinatorial game theory, one of the fields to which Elwyn Berlekamp has made enormous contributions.

    Updated on Sep 28, 2015 01:26 PM PDT
  8. Seminar Research Mini-course

    Created on Sep 03, 2015 03:36 PM PDT
  9. Seminar Research Seminar

    Created on Sep 03, 2015 03:51 PM PDT
  10. Seminar Research Mini-course

    Created on Sep 03, 2015 03:37 PM PDT
  11. Seminar Research Mini-course

    Created on Sep 03, 2015 03:38 PM PDT
  12. Seminar Research Seminar

    Created on Sep 03, 2015 03:52 PM PDT
  13. Seminar Research Mini-course

    Created on Sep 03, 2015 03:40 PM PDT
  14. Seminar Research Mini-course

    Created on Sep 03, 2015 03:41 PM PDT
  15. Seminar Research Seminar

    Created on Sep 03, 2015 03:54 PM PDT
  16. Seminar Research Mini-course

    Created on Sep 03, 2015 03:43 PM PDT
  17. Seminar Research Seminar

    Created on Sep 03, 2015 03:55 PM PDT
  18. Seminar Research Mini-course

    Created on Sep 03, 2015 03:44 PM PDT
  19. Seminar Research Seminar

    Created on Sep 03, 2015 03:56 PM PDT
  20. Program Differential Geometry

    Organizers: Tobias Colding (Massachusetts Institute of Technology), Simon Donaldson (Imperial College, London), John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin-Madison)

    Differential geometry is a subject with both deep roots and recent advances. Many old problems in the field have recently been solved, such as the Poincaré and geometrization conjectures by Perelman, the quarter pinching conjecture by Brendle-Schoen, the Lawson Conjecture by Brendle, and the Willmore Conjecture by Marques-Neves. The solutions of these problems have introduced a wealth of new techniques into the field. This semester-long program will focus on the following main themes:
    (1) Einstein metrics and generalizations,
    (2) Complex differential geometry,
    (3) Spaces with curvature bounded from below,
    (4) Geometric flows,
    and particularly on the deep connections between these areas.

    Updated on Apr 21, 2015 03:40 PM PDT
  21. Workshop Connections for Women: Differential Geometry

    Organizers: Christine Breiner (Fordham University), LEAD Natasa Sesum (Rutgers University)

    The purpose of this meeting is to help junior female researchers to become familiar with the focus topics of the main MSRI program, and also for the junior researchers to have an opportunity to get acquainted with more senior women researchers in differential geometry.

    This workshop is open to all mathematicians.

    Updated on Sep 04, 2015 09:27 AM PDT
  22. Workshop Introductory Workshop: Modern Riemannian Geometry

    Organizers: LEAD Tobias Colding (Massachusetts Institute of Technology), John Lott (University of California, Berkeley), Jeff Viaclovsky (University of Wisconsin-Madison)

    The week will be devoted to an introduction to modern techniques in Riemannian geometry. This is intended to help graduate students and younger researchers get a headstart, in order to increase their participation during the main semester programs and research lectures. To increase outreach, the week will focus on Riemannian geometry and should be largely accessible. Some minicourses on topics of recent interest will be included. The workshop will also have semi-expository lectures dealing with aspects of spaces with curvature bounded from below, since such spaces will occur throughout the semester. We expect that many Berkeley mathematicians and students will participate in the introductory workshop.

    Updated on Aug 25, 2015 05:05 PM PDT
  23. Workshop Kähler Geometry, Einstein Metrics, and Generalizations

    Organizers: Olivier Biquard (École Normale Supérieure), Simon Donaldson (Imperial College, London), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin-Madison)

    The workshop will integrate elements from complex differential geometry with Einstein metrics and their generalizations. The topics will include

    - Existence of Kähler-Einstein metrics and extremal Kähler metrics. Notions of stability in algebraic geometry such as Chow stability, K-stability, b-stability, and polytope stability. Kähler-Einstein metrics with conical singularities along a divisor.

    - Calabi-Yau metrics and collapsed limit spaces. Connections with physics and mirror symmetry.

    - Einstein metrics and their moduli spaces, ε-regularity, noncompact examples such as ALE, ALF, and Poincaré-Einstein metrics. Generalizations of the Einstein condition, such as Bach-flat metrics and Ricci solitons.

    - Sasaki-Einstein metrics and metrics with special holonomy. New examples and classification problems.

    Updated on Sep 15, 2015 03:05 PM PDT
  24. Workshop Hot Topics: Cluster algebras and wall-crossing

    Organizers: LEAD Mark Gross (University of California, San Diego), Paul Hacking, Sean Keel, Lauren Williams (University of California, Berkeley)

    Cluster algebras were introduced in 2001 by Fomin and Zelevinsky to capture the combinatorics of canonical bases and total positivity in semisimple Lie groups. Since then they have revealed a rich combinatorial and group-theoretic structure, and have had significant impact beyond these initial subjects, including string theory, algebraic geometry, and mirror symmetry. Recently Gross, Hacking, Keel and Kontsevich released a preprint introducing mirror symmetry techniques into the subject which resolved several long-standing conjectures, including the construction of canonical bases for cluster algebras and positivity of the Laurent phenomenon. This preprint reformulates the basic construction of cluster algebras in terms of scattering diagrams (or wall-crossing structures). This leads to the proofs of the conjectures and to new constructions of elements of cluster algebras. But fundamentally they provide a new tool for thinking about cluster algebras.

    The workshop will bring together many of the different users of cluster algebras to achieve a synthesis of these new techniques with many of the different aspects of the subject. There will be lecture series on the new techniques, and other lecture series on connections with Lie theory, quiver representation theory, mirror symmetry, string theory, and stability conditions.

    Updated on Aug 06, 2015 08:56 AM PDT
  25. Workshop Geometric Flows in Riemannian and Complex Geometry

    Organizers: Tobias Colding (Massachusetts Institute of Technology), LEAD John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University)

    The workshop will concentrate on parabolic methods in both Riemannian and complex geometry. The topics will include

    - Ricci flow. Analytic questions about Ricci flow in three dimensions. Possible applications of Ricci flow to 4-manifold topology. Ricci flow in higher dimensions under curvature assumptions.

    - Kähler-Ricci Flow. Applications to the Kähler-Einstein problem. Connections to the minimal model program. Study of Kähler-Ricci solitons and limits of Kähler-Ricci flow.

    - Mean curvature flow. Singularity analysis. Generic mean curvature flow.

    - Other geometric flows such as Calabi flow and pluriclosed flow.

    Updated on Sep 16, 2015 12:34 PM PDT
  26. Summer Graduate School Seminaire de Mathematiques Superieures 2016: Dynamics of Biological Systems

    Organizers: Thomas Hillen (University of Alberta), Mark Lewis (University of Alberta), Yingfei Yi (University of Alberta)

    Analysis of biological dynamics is rapidly growing, from both mathematical and biological perspectives. While solidly grounded in the theory of nonlinear dynamical systems, the interplay between mathematics and biological systems has been fertile ground for new developments.  Participants of the school will be exposed to foundational theory as well as a broad spectrum of new developments in dynamics of biological systems. The summer school will prepare students for new original research in the field. The summer school structure involves 12 lecture sequences for around 60 students, spread over two weeks.

    Updated on Sep 23, 2015 01:37 PM PDT
  27. MSRI-UP MSRI-UP 2016: Sandpile Groups

    Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Herbert Medina (Loyola Marymount University), LEAD Suzanne Weekes (Worcester Polytechnic Institute)

    The MSRI-UP summer program is designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply and the program cannot accept foreign students regardless of funding. The academic portion of the 2016 program will be led by Prof. Luis Garcia-Puente of Sam Houston State University.

    Updated on Oct 02, 2015 01:38 PM PDT
  28. Summer Graduate School Harmonic Analysis and Elliptic Equations on real Euclidean Spaces and on Rough Sets

    Organizers: LEAD Steven Hofmann (University of Missouri), Jose Maria Martell (Instituto de Ciencias Matematicas)

    The goal of the workshop is to present harmonic analysis techniques in $R^n$ (the ``flat" setting), and then to show how those techniques extend to much rougher settings, with application to the theory of elliptic equations. Thus, the subject matter of the workshop will introduce the students to an active, current research area:  the interface between harmonic analysis, elliptic PDE, and geometric measure theory.

    Updated on Sep 23, 2015 01:37 PM PDT
  29. Summer Graduate School An Introduction to Character Theory and the McKay Conjecture

    Organizers: Robert Guralnick (University of Southern California), Pham Tiep (University of Arizona)

    Character Theory of Finite Groups provides one of the most powerful tools to study groups. In this course we will give a gentle introduction to basic results in the Character Theory, as well as some of the main conjectures in Group Representation Theory, with particular emphasis on the McKay Conjecture.

    Updated on Sep 23, 2015 01:38 PM PDT
  30. Summer Graduate School Electronic Structure Theory

    Organizers: LEAD Lin Lin (University of California, Berkeley), Jianfeng Lu (Duke University), James Sethian (University of California, Berkeley)

    Ab initio or first principle electronic structure theories, particularly represented by Kohn-Sham density functional theory (KS-DFT), have been developed into workhorse tools with a wide range of scientific applications in chemistry, physics, materials science, biology etc. What is needed are new techniques that greatly extend the applicability and versatility of these approaches. At the core, many of the challenges that need to be addressed are essentially mathematical. The purpose of the workshop is to provide graduate students a self-contained introduction to electronic structure theory, with particular emphasis on frontier topics in aspects of applied analysis and numerical methods. 

    Updated on Sep 23, 2015 01:38 PM PDT
  31. Summer Graduate School Chip Firing and Tropical Curves

    Organizers: LEAD Matthew Baker (Georgia Institute of Technology), Melody Chan (Harvard University), Sam Payne (Yale University)

    Tropical geometry uses a combination of techniques from algebraic geometry, combinatorics, and convex polyhedral geometry to study degenerations of algebraic varieties; the simplest tropical objects are tropical curves, which one can think of as "shadows" of algebraic curves.  Linear equivalence of divisors on an abstract tropical curve is determined by a simple but rich combinatorial process called "chip firing", which was discovered independently in the discrete setting by physicists and graph theorists.  From a pedagogical point of view, one can view tropical curves as a combinatorial model for the highly analogous but more abstract theory of algebraic curves, but there is in fact much more to the story than this: one can use tropical curves and chip firing to prove theorems in algebraic geometry and number theory.  This field is relatively new, so participants will have the opportunity to start from scratch and still get a glimpse of the cutting edge in this active research area.

    Updated on Sep 23, 2015 01:39 PM PDT
  32. Program Geometric Group Theory

    Organizers: Ian Agol (University of California, Berkeley), Mladen Bestvina (University of Utah), Cornelia Drutu (University of Oxford), LEAD Mark Feighn (Rutgers University), Michah Sageev (Technion---Israel Institute of Technology), Karen Vogtmann (Cornell University)

    The field of geometric group theory emerged from Gromov’s insight that even mathematical objects such as groups, which are defined completely in algebraic terms, can be profitably viewed as geometric objects and studied with geometric techniques Contemporary geometric group theory has broadened its scope considerably, but retains this basic philosophy of reformulating in geometric terms problems from diverse areas of mathematics and then solving them with a variety of tools. The growing list of areas where this general approach has been successful includes low-dimensional topology, the theory of manifolds, algebraic topology, complex dynamics, combinatorial group theory, algebra, logic, the study of various classical families of groups, Riemannian geometry and representation theory.

    The goals of this MSRI program are to bring together people from the various branches of the field in order to consolidate recent progress, chart new directions, and train the next generation of geometric group theorists.

    Updated on Jul 15, 2015 10:57 AM PDT
  33. Workshop Connections for Women: Geometric Group Theory

    Organizers: LEAD Ruth Charney (Brandeis University), Indira Chatterji (Université de Nice Sophia Antipolis), Mark Feighn (Rutgers University), Talia Fernos (University of North Carolina)

    This three-day workshop will feature talks by six prominent female mathematicians on a wide range of topics in geometric group theory.  Each speaker will give two lectures, separated by a break-out session during which participants will meet in small groups to discuss ideas presented in the first lecture.   The workshop is open to all mathematicians. 

    Updated on Sep 10, 2015 11:50 AM PDT
  34. Workshop Introductory Workshop: Geometric Group Theory

    Organizers: Martin Bridson (University of Oxford), Benson Farb (University of Chicago), LEAD Zlil Sela (Hebrew University), Karen Vogtmann (Cornell University)

    This will be an introductory workshop to the MSRI jumbo program Geometric Group Theory being held during the Fall Semester of 2016. The purpose of the workshop is to provide an overview of key areas of research to be covered in the program, including an introduction to open problems of current interest.

    Updated on Jul 27, 2015 03:36 PM PDT
  35. Workshop Groups acting on CAT(0) spaces

    Organizers: Ian Agol (University of California, Berkeley), Pierre-Emmanuel Caprace (Université Catholique de Louvain), Koji Fujiwara (Kyoto University), Alessandra Iozzi (ETHZ), LEAD Michah Sageev (Technion---Israel Institute of Technology)

    The theme of the workshop is algebraic, geometric and analytical aspects of groups that act by isometries on spaces of non-positive curvature known as CAT(0) spaces. The world of CAT(0) spaces includes classical spaces such as symmetric spaces and buildings, as well as more avant-garde arrivals, such as CAT(0) cube complex. The workshop will bring together researchers studying various aspects of such groups and spaces to discuss recent developments and chart new directions in the field. 

    Updated on Aug 14, 2015 01:41 PM PDT
  36. Workshop Amenability, coarse embeddability and fixed point properties

    Organizers: Goulnara Arzhantseva (University of Vienna), LEAD Cornelia Drutu (University of Oxford), Graham Niblo (University of Southampton), Piotr Nowak (Polish Academy of Sciences)

    The main theme of the workshop is the spectrum of analytic properties running from Kazhdan's property (T) at one end to von Neumann's amenability at the other, that forms a foundational organizing structure for infinite groups and spaces. These properties can be described both analytically, via unitary representation theory, and geometrically, using embedding properties for discrete spaces. Connections with probability and combinatorics will likewise be addressed during the meeting.

    Updated on Sep 02, 2015 10:15 AM PDT
  37. Program Analytic Number Theory

    Organizers: Chantal David (Concordia University), Andrew Granville (Université de Montréal), Emmanuel Kowalski (Eidgenössische TH Zürich-Hönggerberg), Philippe Michel (École Polytechnique Fédérale de Lausanne (EPFL)), Kannan Soundararajan (Stanford University), LEAD Terence Tao (University of California, Los Angeles)

    Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking problems in other fields.

    This program will not only give the leading researchers in the area further opportunities to work together, but more importantly give young people the occasion to learn about these topics, and to give them the tools to achieve the next breakthroughs.

    Updated on Jul 10, 2015 03:54 PM PDT
  38. Program Harmonic Analysis

    Organizers: LEAD Michael Christ (University of California, Berkeley), Allan Greenleaf (University of Rochester), Steven Hofmann (University of Missouri), LEAD Michael Lacey (Georgia Institute of Technology), Svitlana Mayboroda (University of Minnesota, Twin Cities), Betsy Stovall (University of Wisconsin-Madison), Brian Street (University of Wisconsin-Madison)

    The field of Harmonic Analysis dates back to the 19th century, and has its roots in the study of the decomposition of functions using Fourier series and the Fourier transform.  In recent decades, the subject has undergone a rapid diversification and expansion, though the decomposition of functions and operators into simpler parts remains a central tool and theme.  
    This program will bring together researchers representing the breadth of modern Harmonic Analysis and will seek to capitalize on and continue recent progress in four major directions:
         -Restriction, Kakeya, and Geometric Incidence Problems
         -Analysis on Nonhomogeneous Spaces
         -Weighted Norm Inequalities
         -Quantitative Rectifiability and Elliptic PDE.
    Many of these areas draw techniques from or have applications to other fields of mathematics, such as analytic number theory, partial differential equations, combinatorics, and geometric measure theory.  In particular, we expect a lively interaction with the concurrent program.  

    Updated on Jun 08, 2015 04:00 PM PDT
  39. Workshop Connections for Women: Harmonic Analysis

    Organizers: LEAD Svitlana Mayboroda (University of Minnesota, Twin Cities), Betsy Stovall (University of Wisconsin-Madison)

    This workshop will highlight the work of several prominent women working in harmonic analysis, including some of the field's rising stars.  It will feature 3 mini courses by senior researchers, a number of talks by analysts at the postdoctoral level and above, and a poster session for graduate students.   This workshop is open to all mathematicians.

    Updated on Sep 04, 2015 11:35 AM PDT
  40. Workshop Introductory Workshop: Harmonic Analysis

    Organizers: Allan Greenleaf (University of Rochester), Steven Hofmann (University of Missouri), LEAD Michael Lacey (Georgia Institute of Technology), Betsy Stovall (University of Wisconsin-Madison)

    This week-long workshop will serve as an introduction for graduate students, postdocs, and other researchers to the main themes of the program.  It will feature accessible talks by a number of leading harmonic analysts, including several short courses on the core ideas and techniques in the field.  There will also be a problem session, to which all participants are encouraged to contribute. 

    Updated on Sep 04, 2015 11:08 AM PDT
  41. Workshop Recent developments in analytic number theory

    Organizers: Timothy Browning (University of Bristol), Chantal David (Concordia University), Kannan Soundararajan (Stanford University), LEAD Terence Tao (University of California, Los Angeles)

    This workshop will be focused on presenting the latest developments in analytic number theory, including (but not restricted to) recent advances in sieve theory, multiplicative number theory, exponential sums, arithmetic statistics, estimates on automorphic forms, and the Hardy-Littlewood circle method.

    Updated on Sep 11, 2015 12:25 PM PDT
  42. Workshop Recent Developments in Harmonic Analysis

    Organizers: Michael Christ (University of California, Berkeley), LEAD Michael Lacey (Georgia Institute of Technology), Svitlana Mayboroda (University of Minnesota, Twin Cities), Brian Street (University of Wisconsin-Madison)

    Topics for this workshop will be drawn from the main research directions of this conference, including:
    (1) Restriction, Kakeya, and geometric incidence problems 
    (2) Analysis on nonhomogenous spaces
    (3) Weighted estimates
    (4) Quantitative rectifiability and other topics in PDE

    Updated on Sep 01, 2015 05:01 PM PDT
  43. Program Geometric and Topological Combinatorics

    Organizers: Jesus De Loera (University of California, Davis), Vic Reiner (University of Minnesota Twin Cities), LEAD Francisco Santos (University of Cantabria), Francis Su (Harvey Mudd College), Rekha Thomas (University of Washington), Günter M. Ziegler (Freie Universität Berlin)

    Combinatorics is one of the fastest growing areas in contemporary Mathematics, and much of this growth is due to the connections and interactions with other areas of Mathematics. This program is devoted to the very vibrant and active area of interaction between Combinatorics with Geometry and Topology. That is, we focus on (1) the study of the combinatorial properties or structure of geometric and topological objects and (2) the development of geometric and topological techniques to answer combinatorial problems.

    Key examples of geometric objects with intricate combinatorial structure are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. Examples of topology in action answering combinatorial challenges are the by now classical Lovász’s solution of the Kneser conjecture, which yielded functorial approaches to graph coloring, and the  more recent, extensive topological machinery leading to breakthroughs on Tverberg-type problems.

    Updated on Sep 15, 2015 02:18 PM PDT
  44. Program Geometric Functional Analysis and Applications

    Organizers: Franck Barthe (Universite Paul Sabatier--Toulouse III), Marianna Csornyei (University of Chicago), Boaz Klartag (Tel Aviv University), Alexander Koldobsky (University of Missouri), Rafal Latala (University of Warsaw), LEAD Mark Rudelson (University of Michigan)

    Geometric functional analysis lies at the interface of convex geometry, functional analysis and probability. It has numerous applications ranging from geometry of numbers and random matrices in pure mathematics to geometric tomography and signal processing in engineering and numerical optimization and learning theory in computer science.

    One of the directions of the program is classical convex geometry, with emphasis on connections with geometric tomography, the study of geometric properties of convex bodies based on information about their sections and projections. Methods of harmonic analysis play an important role here. A closely related direction is asymptotic geometric analysis studying geometric properties of high dimensional objects and normed spaces, especially asymptotics of their quantitative parameters as dimension tends to infinity. The main tools here are concentration of measure and related probabilistic results. Ideas developed in geometric functional analysis have led to progress in several areas of applied mathematics and computer science, including compressed sensing and random matrix methods. These applications as well as the problems coming from computer science will be also emphasised in our program.

    Updated on Jun 02, 2015 01:17 PM PDT
  45. Workshop Geometric and topological combinatorics: Modern techniques and methods

    Organizers: Patricia Hersh (North Carolina State University), LEAD Vic Reiner (University of Minnesota Twin Cities), Bernd Sturmfels (UC Berkeley Math Faculty), Frank Vallentin (Universität zu Köln), Günter M. Ziegler (Freie Universität Berlin)

    This workshop will focus on the interaction between Combinatorics, Geometry and Topology, including recent developments and techniques in areas such as 

    -- polytopes and cell complexes,
    -- simplicial complexes and higher order graph theory,
    -- methods from equivariant topology and configuration spaces,

    -- geometric combinatorics in optimization and social choice theory,
    -- algebraic and algebro-geometric methods.

    Updated on Sep 18, 2015 02:54 PM PDT
  46. Workshop Geometric functional analysis and applications

    Organizers: Franck Barthe (Universite Paul Sabatier--Toulouse III), Rafal Latala (University of Warsaw), Emanuel Milman (Technion---Israel Institute of Technology), Assaf Naor (Princeton University), LEAD Gideon Schechtman (Weizmann Institute of Science)

    This is the main workshop of the program "Geometric functional analysis and applications". It will focus on the main topics of the program. These include: Convex geometry, Asymptotic geometric analysis, Interaction with computer science, Signal processing, Random matrix theory and other aspects of Probability.

    Created on Sep 10, 2015 11:41 AM PDT
  47. Program Enumerative Geometry Beyond Numbers

    Organizers: Mina Aganagic (University of California, Berkeley), Denis Auroux (University of California, Berkeley), Jim Bryan, LEAD Andrei Okounkov (Columbia University), Balazs Szendroi

    Traditional enumerative geometry asks certain questions to which the expected answer is a number: for instance, the number of lines incident with two points in the plane (1, Euclid), or the number of twisted cubic curves on a quintic threefold (317 206 375). It has however been recognized for some time that the numerics is often just the tip of the iceberg: a deeper exploration reveals interesting geometric, topological, representation-, or knot-theoretic structures. This semester-long program will be devoted to these hidden structures behind enumerative invariants, concentrating on the core fields where these questions start: algebraic and symplectic geometry.

    Updated on Sep 18, 2015 01:27 PM PDT
  48. Program Group Representation Theory and Applications

    Organizers: Robert Guralnick (University of Southern California), Alexander (Sasha) Kleshchev (University of Oregon), Gunter Malle (Universität Kaiserslautern), Gabriel Navarro (University of Valencia), Julia Pevtsova (University of Washington), Raphael Rouquier (University of California, Los Angeles), LEAD Pham Tiep (University of Arizona)

    Group Representation Theory is a central area of Algebra, with important and deep connections to areas as varied as topology, algebraic geometry, number theory, Lie theory, homological algebra, and mathematical physics. Born more than a century ago, the area still abounds with basic problems and fundamental conjectures, some of which have been open for over five decades. Very recent breakthroughs have led to the hope that some of these conjectures can finally be settled. In turn, recent results in group representation theory have helped achieve substantial progress in a vast number of applications.

    The goal of the program is to investigate all these deep problems and the wealth of new results and directions, to obtain major progress in the area, and to explore further applications of group representation theory to other branches of mathematics.

    Updated on Apr 10, 2015 02:52 PM PDT
  49. Workshop Representations of Finite and Algebraic Groups

    Organizers: Robert Guralnick (University of Southern California), Alexander (Sasha) Kleshchev (University of Oregon), Gunter Malle (Universität Kaiserslautern), Gabriel Navarro (University of Valencia), LEAD Pham Tiep (University of Arizona)

    The workshop will bring together key researchers working in various areas of Group Representation Theory to strengthen the interaction and collaboration between them and to make further progress on a number of
    basic problems and conjectures in the field. Topics of the workshop include
    -- Global-local conjectures in the representation theory of finite groups
    -- Representations and cohomology of simple, algebraic and finite groups
    -- Connections to Lie theory and categorification, and
    -- Applications to group theory, number theory, algebraic geometry, and combinatorics.

    Updated on Oct 02, 2015 04:31 PM PDT

Past Scientific Events

  1. Workshop Elementary Introduction to the Langlands Program, by Edward Frenkel

    Organizers: Edward Frenkel (University of California, Berkeley)

    One of the most fascinating and important developments in mathematics in the last 50 years is the "Langlands Program", a collection of ideas that provides a grand unification of many areas of mathematics. Frenkel's celebrated book "Love and Math", now translated into many languages, provides an extraordinarily accessible overview of the deep mathematics involved. The lectures will be a great opportunity to hear the story of these ideas from a great expositor, and participate in a discussion of them. Covering topics from the basic ideas of symmetries and Fermat's last theorem to the recent works connecting the Langlands Program to dualities in quantum physics, the lectures will be accessible to undergraduate students.

    Updated on Sep 16, 2015 02:28 PM PDT
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